Abstract
Ab initio kinetic Monte Carlo (KMC) simulations have been successfully applied for over two decades to elucidate the underlying physico-chemical phenomena on the surfaces of heterogeneous catalysts. These simulations necessitate detailed knowledge of the kinetics of elementary reactions constituting the reaction mechanism, and the energetics of the species participating in the chemistry. The information about the energetics is encoded in the formation energies of gas and surface-bound species, and the lateral interactions between adsorbates on the catalytic surface, which can be modeled at different levels of detail. The majority of previous works accounted for only pairwise-additive first nearest-neighbor interactions. More recently, cluster-expansion Hamiltonians incorporating long-range interactions and many-body terms have been used for detailed estimations of catalytic rate [C. Wu, D. J. Schmidt, C. Wolverton, and W. F. Schneider, J. Catal. 286, 88 (2012)]. In view of the increasing interest in accurate predictions of catalytic performance, there is a need for general-purpose KMC approaches incorporating detailed cluster expansion models for the adlayer energetics. We have addressed this need by building on the previously introduced graph-theoretical KMC framework, and we have developed Zacros, a FORTRAN2003 KMC package for simulating catalytic chemistries. To tackle the high computational cost in the presence of long-range interactions we introduce parallelization with OpenMP. We further benchmark our framework by simulating a KMC analogue of the NO oxidation system established by Schneider and co-workers [J. Catal. 286, 88 (2012)]. We show that taking into account only first nearest-neighbor interactions may lead to large errors in the prediction of the catalytic rate, whereas for accurate estimates thereof, one needs to include long-range terms in the cluster expansion.
Highlights
The origins of temporal investigations of processes on lattices can be sought in the seminal work by Glauber, who analyzed a Markov process for spin flips in the Ising Model, back in 1963.1 The subsequent development of kinetic Monte Carlo approaches[2,3] enabled the study of complex timedependent phenomena in the Ising model such as metastability and dynamic critical phenomena
To enable the coupling with ab initio calculations for a first-principles based simulation of chemistries on catalytic surfaces[16–31]. In these firstprinciples kinetic Monte Carlo (KMC) frameworks the reaction energies and activation barriers are typically obtained from density functional theory (DFT) calculations, and the kinetic parameters are calculated by employing transition state theory (TST) approximations
Within the level of accuracy of DFT and to the extent of validity of TST, the quality of the predictions obtained by KMC depends on “how well” the ab initio data have been incorporated into the simulation
Summary
The origins of temporal investigations of processes on lattices can be sought in the seminal work by Glauber, who analyzed a Markov process for spin flips in the Ising Model, back in 1963.1 The subsequent development of kinetic Monte Carlo approaches[2,3] enabled the study of complex timedependent phenomena in the Ising model such as metastability and dynamic critical phenomena (see for instance Refs. 4–7). First-principles KMC frameworks used DFT and bond-order conservation (BOC) methods to account for such effects.[16,17]. In some instances, such interactions were neglected altogether or modeled by pairwise additive nearest neighbor contributions, due to large computational expense needed for implementing more accurate models.[36]. The most general such models consist of cluster-expansion (CE) Hamiltonians, which can accommodate any level of accuracy by taking into account
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